{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A study on spontaneous decay rate of an atom in presence of a nanofiber using BEM approach\n",
    "\n",
    "In these notes, I calculate the Local Density of States (LDOS), or the imaginary part of the on-site Green's function and hence the modified spontaneous emission rate of an atom in presence of a nanofiber using the Boundary Element Method (BEM). The BEM code is from Prof. Alejandro Manjavacas's group. \n",
    "\n",
    "This is an [IJulia notebook](https://github.com/JuliaLang/IJulia.jl), which provides a nice\n",
    "browser-based [Jupyter](http://jupyter.org/) interface to the [Julia language](http://julialang.org/), a high-level dynamic language (similar to Matlab or Python+SciPy) for technical computing.  The notebook allows us to combine code and results in one place.\n",
    "\n",
    "We are only manipulating the generated data from the simulation results in this notebook. As a brief recap of the simulation process, I have used a compiled BEM code by Alejandro's group written in C++ called `bem2D` on a cluster computing system. A configuration C++ code is defined in the files `nanofiber_dipolex_new.cpp`, `nanofiber_dipoley_new.cpp` and `nanofiber_dipolez_new.cpp` which are put in the same folder as `bem2D`. We fix the wavelength of the light as the `D_2` line or `852`nm. The only changing parameter is the atom position `x=n` in the units of nm to calculate the Green's function tensor and radiation decay rates of atom at different positions. So, I wrote a bash script to change the atom positions according to a given list of `x`-position. \n",
    "Then run the bash script as follows to generate corresponding executables and to submit the generated PBS scripts to the cluster system/workstation to run the simulations:\n",
    "```\n",
    "bash ./quickreplacesubmitjobs.sh\n",
    "```\n",
    "All geometry and simuation data files are dumped to the `./nanofiberD2` subfolder under the same folder as all other C++ and bash scripts. Notice that the name of the generated PBS scripts and data files is automatically generated based on the configuration parameters for the simulations. The induced local E-field simulation data files have a `.dat` extension; there are another two `*.dat` files for the geometry of boundary and dieletric function distribution, which have been plotted out in the `nanofiber_BEM.ipynb` notebook. The actual simulation was done on the `NapaValley` workstation. We will only extract the data for the local E-field and the corresponding Green's function and decay rates for the radiative mode contributions in this notebook.\n",
    "\n",
    "For the following code, I have transfered all induced E-field data files to the `/data/D2` folder.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can read in this data as a matrix of numbers by the `readdlm` function in Julia with the `header=false` option meaning that it reads the first line as the beginning of the data entries without a list of strings describing each column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot the results.  I'll use the [PyPlot](https://github.com/stevengj/PyPlot.jl) package in Julia, which is an interface to the sophisticated [matplotlib](http://matplotlib.org/) Python plotting library.   We'll plot three things:\n",
    "\n",
    "* Calculate the Green's function tensor and waveguide-modified spontaneous decay rates from the radiative modes when the dipole varies its position outside of the waveguide.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the boundary and index of refraction profile of the waveguide in the xy cross section\n",
    "\n",
    "Our boundary points are meshed in the files `/data/geom_a_225.data` and `/data/geom_regions_a_225.data`, which positions where the equivalent charges and current sources to be computed in the BEM simulation. The waveguide has a circular cross-section of a radius $a=225nm$ ($nm$ is the unit of length) and a index of refraction of $n_1=n_{core}=1.4496$ for the waveguide material and $n_2=n_{clad}=1$ for the vacuum clad. \n",
    "\n",
    "It is good to plot out the mesh of index of refraction in space and find out how good is the mesh resolution. This can be done by plotting out the output eps file in a simple data table format, which ends in `.dat`. \n",
    "\n",
    "The following will first print out some of the data in order to figure out the physics meaning of the dimensions. They should contain the coordinate and index of refraction information for the simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the modified decay rates, we need to use the LDOS value at the dipole position. The result is calculated at a series of $k$ points. I expect to see a continuous positive curve when $k\\in [0,1]\\omega/c$ or in the radiative mode regime and a single positive spark in the $[1,1.45]\\omega/c$ or guided mode regime--given the waveguide is a single-mode glass fiber."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the result above was calculated using a $k$-resolution of $\\Delta k= 0.01k_0$. We can compare the results above with a coarser/finer gridding cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the known Green's function tensor expression for the guided modes, one can hence obtain a precise enough result for the decay rates as a function of dipole orientation and atom position."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Calculation of Green's function tensor using BEM\n",
    "\n",
    "BEM can output full local field components so that computing the radiative mode contribution to the full Green's function tensor is possible. With the Green's function tensor, one can then calculate the modified decay rates with dipoles orientated along arbitrary directions--including the dipole transitions corresponding to $\\sigma_\\pm$ and $\\pi$ transitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f650547a4d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "40-element Array{Float64,1}:\n",
       " 1.29134 \n",
       " 1.21289 \n",
       " 1.16422 \n",
       " 1.12397 \n",
       " 1.09003 \n",
       " 1.0614  \n",
       " 1.03739 \n",
       " 1.01743 \n",
       " 1.00106 \n",
       " 0.987891\n",
       " 0.97756 \n",
       " 0.96976 \n",
       " 0.964205\n",
       " ⋮       \n",
       " 1.00534 \n",
       " 1.00924 \n",
       " 1.0127  \n",
       " 1.01567 \n",
       " 1.01812 \n",
       " 1.02003 \n",
       " 1.02141 \n",
       " 1.02224 \n",
       " 1.02255 \n",
       " 1.02235 \n",
       " 1.02168 \n",
       " 1.02058 "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load data for different dipole positions.\n",
    "rp_BEM=[230,240,250,260,270,280,290,300,310,320,330,340,350,360,370,380,390,400,405,410,420,430,440,450,460,470,480,490,500,510,520,530,540,550,560,570,580,590,600,610];\n",
    "lenrp=length(rp_BEM);\n",
    "lendr=146;\n",
    "a=225;\n",
    "E_dipolex = readdlm(\"data/D2/dipolex_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_405_y_0_q_0_1.45_146.dat\", header=false);\n",
    "k_vec=E_dipolex[:,2];\n",
    "Ex_dx=zeros(Complex{Float64},lendr,lenrp); Ey_dx=zeros(Complex{Float64},lendr,lenrp); Ez_dx=zeros(Complex{Float64},lendr,lenrp);\n",
    "Ex_dy=zeros(Complex{Float64},lendr,lenrp); Ey_dy=zeros(Complex{Float64},lendr,lenrp); Ez_dy=zeros(Complex{Float64},lendr,lenrp);\n",
    "Ex_dz=zeros(Complex{Float64},lendr,lenrp); Ey_dz=zeros(Complex{Float64},lendr,lenrp); Ez_dz=zeros(Complex{Float64},lendr,lenrp);\n",
    "for ii=1:lenrp\n",
    "    E_dipolex = readdlm(\"data/D2/dipolex_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_$(rp_BEM[ii])_y_0_q_0_1.45_146.dat\", header=false)\n",
    "    Ex_dx[:,ii]=E_dipolex[:,5]+im*E_dipolex[:,6];\n",
    "    Ey_dx[:,ii]=E_dipolex[:,7]+im*E_dipolex[:,8];\n",
    "    Ez_dx[:,ii]=E_dipolex[:,9]+im*E_dipolex[:,10];\n",
    "    \n",
    "    E_dipoley = readdlm(\"data/D2/dipoley_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_$(rp_BEM[ii])_y_0_q_0_1.45_146.dat\", header=false)\n",
    "    Ex_dy[:,ii]=E_dipoley[:,5]+im*E_dipoley[:,6];\n",
    "    Ey_dy[:,ii]=E_dipoley[:,7]+im*E_dipoley[:,8];\n",
    "    Ez_dy[:,ii]=E_dipoley[:,9]+im*E_dipoley[:,10];\n",
    "    \n",
    "    E_dipolez = readdlm(\"data/D2/dipolez_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_$(rp_BEM[ii])_y_0_q_0_1.45_146.dat\", header=false)\n",
    "    Ex_dz[:,ii]=E_dipolez[:,5]+im*E_dipolez[:,6];\n",
    "    Ey_dz[:,ii]=E_dipolez[:,7]+im*E_dipolez[:,8];\n",
    "    Ez_dz[:,ii]=E_dipolez[:,9]+im*E_dipolez[:,10];\n",
    "end\n",
    "# Calculate the diagonal elements of the Green's function tensor from the radiation mode contribution.\n",
    "c=2.99792458e8;\n",
    "au=1.72e7; # This is the atomic unit in the CGS-units: $q/a_0^2$ statvolts/cm. In SI units, it becomes $e/(4π\\varepsilon_0a_0^2)$ = 5.2e11 V/m.\n",
    "lambda0=0.852e-6;\n",
    "ω=2.*pi*c/lambda0;\n",
    "GFT_rad_ind=zeros(Complex{Float64},3,3,lenrp);\n",
    "Gxx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gxy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gxz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gyz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzx_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzy_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "Gzz_rad_ind=zeros(Complex{Float64},lenrp);\n",
    "G0=Inf + 2.0/3.*(ω/c)^3*im;\n",
    "gamma_rad_BEM_rp_average=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_sigmap=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_sigmam=zeros(lenrp);\n",
    "gamma_rad_BEM_rp_pi=zeros(lenrp);\n",
    "# Define the unitary dipole orientation vector.\n",
    "e_dipole_sigmap=[-1.;-1.0*im;0]/sqrt(2);\n",
    "e_dipole_sigmam=[1.; -1.0*im;0]/sqrt(2);\n",
    "e_dipole_pi=[0.; 0.; 1.];\n",
    "using NumericalIntegration # For calculating the integral over k in the range of [0,1]k_0 to obtain the radiative mode contributions to GFT and decay rates.\n",
    "breakpoint=100; # This is the index number where the radiative mode cut off out of the k in [0,1]k_0 range.  \n",
    "for ii=1:lenrp\n",
    "    Gxx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gyy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gzz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;#G0+\n",
    "    Gyx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gzx_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dx[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gxy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gzy_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ez_dy[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gxz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ex_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    Gyz_rad_ind[ii]=integrate(k_vec[1:breakpoint],Ey_dz[1:breakpoint,ii],Trapezoidal())*(ω/c)^3/pi^2*au*4.0/3.;\n",
    "    GFT_rad_ind[:,:,ii]=[Gxx_rad_ind[ii] Gxy_rad_ind[ii] Gxz_rad_ind[ii];\n",
    "        Gyx_rad_ind[ii] Gyy_rad_ind[ii] Gzy_rad_ind[ii];\n",
    "        Gzx_rad_ind[ii] Gzy_rad_ind[ii] Gzz_rad_ind[ii]];\n",
    "end\n",
    "\n",
    "# Calculate the relative averaged decay rate at the given dipole located at x=405nm and y=0.\n",
    "gamma0=imag(G0);\n",
    "for ii =1:lenrp\n",
    "    gamma_rad_BEM_rp_average[ii]=1+trace(imag(GFT_rad_ind[:,:,ii]))/gamma0/3.;\n",
    "    gamma_rad_BEM_rp_sigmap[ii]=1+real((e_dipole_sigmap'*imag(GFT_rad_ind[:,:,ii])*e_dipole_sigmap)/gamma0)[1];\n",
    "    gamma_rad_BEM_rp_sigmam[ii]=1+real((e_dipole_sigmam'*imag(GFT_rad_ind[:,:,ii])*e_dipole_sigmam)/gamma0)[1];\n",
    "    gamma_rad_BEM_rp_pi[ii]=1+real((e_dipole_pi'*imag(GFT_rad_ind[:,:,ii])*e_dipole_pi)/gamma0)[1];\n",
    "end\n",
    "\n",
    "# Recalculate the diagonal GFT elements with a dipole placed at r'=405nm from the fiber axis with lower imaginary part of epsilon.\n",
    "E_dipolex = readdlm(join([\"data/D2/dipolex_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_\",\"405\",\"_y_0_q_0_1.45_146.dat\"]), header=false)\n",
    "Ex_dx_r0=E_dipolex[:,5]+im*E_dipolex[:,6];\n",
    "Ey_dx_r0=E_dipolex[:,7]+im*E_dipolex[:,8];\n",
    "Ez_dx_r0=E_dipolex[:,9]+im*E_dipolex[:,10];\n",
    "E_dipoley = readdlm(join([\"data/D2/dipoley_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_\",\"405\",\"_y_0_q_0_1.45_146.dat\"]), header=false)\n",
    "Ex_dy_r0=E_dipoley[:,5]+im*E_dipoley[:,6];\n",
    "Ey_dy_r0=E_dipoley[:,7]+im*E_dipoley[:,8];\n",
    "Ez_dy_r0=E_dipoley[:,9]+im*E_dipoley[:,10];\n",
    "E_dipolez = readdlm(join([\"data/D2/dipolez_E_N_1_lam_852_eps_2.1013_0.001_a_225_x_\",\"405\",\"_y_0_q_0_1.45_146.dat\"]), header=false)\n",
    "Ex_dz_r0=E_dipolez[:,5]+im*E_dipolez[:,6];\n",
    "Ey_dz_r0=E_dipolez[:,7]+im*E_dipolez[:,8];\n",
    "Ez_dz_r0=E_dipolez[:,9]+im*E_dipolez[:,10];\n",
    "Gxx_rad_r0=integrate(k_vec[1:breakpoint],Ex_dx_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4./3.;\n",
    "Gyy_rad_r0=integrate(k_vec[1:breakpoint],Ey_dy_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4./3.;\n",
    "Gzz_rad_r0=integrate(k_vec[1:breakpoint],Ez_dz_r0[1:breakpoint],Trapezoidal())*(ω/c)^3/pi^2*au*4./3.;\n",
    "gamma_rad_BEM_r0=imag(Gxx_rad_r0+Gyy_rad_r0+Gzz_rad_r0)/3./gamma0;\n",
    "\n",
    "# Plot out gamma_rad as a function of dipole position.\n",
    "using PyPlot\n",
    "figure(figsize=(16,3));\n",
    "subplot(1,2,1)\n",
    "plot((1:breakpoint)/100.,real(Ex_dx[1:breakpoint,4]),\"r-\")\n",
    "plot((1:breakpoint)/100.,imag(Ex_dx[1:breakpoint,4]),\"b-\")\n",
    "ylabel(L\"E(\\beta)\")\n",
    "xlabel(L\"\\beta/k_0\")\n",
    "legend([\"Real\",\"Imag\"],loc=\"lower left\")\n",
    "\n",
    "subplot(1,2,2)\n",
    "a=225.;\n",
    "#plot(rp0_test[1,:]/1.e-9-a, 1+sum(gamma_rad,2), \"r-\", linewidth=2.0)\n",
    "plot(rp_BEM-a,real(gamma_rad_BEM_rp_average),\"b*-\")\n",
    "plot(405-a,real(gamma_rad_BEM_r0)+1.,\"mo\");\n",
    "plot(rp_BEM-a,gamma_rad_BEM_rp_sigmap,\"r.-\");\n",
    "plot(rp_BEM-a,gamma_rad_BEM_rp_sigmam,\"m--\");\n",
    "plot(rp_BEM-a,gamma_rad_BEM_rp_pi,\"k.\")\n",
    "xlabel(\"(r'-a)/nm\")\n",
    "ylabel(L\"\\Gamma_{rad}^{BEM}/\\Gamma_0\")\n",
    "#ylim([0,1.2])\n",
    "legend([L\"average_{BEM}\",L\"average_{no\\,\\,loss}\",L\"\\sigma_+\",L\"\\sigma_-\",L\"\\pi\"],loc=\"upper center\",fontsize=12);\n",
    "#legend([L\"average_{BEM}\",L\"average_{no\\,\\,loss}\",L\"\\sigma_+\",L\"\\sigma_-\",L\"\\pi\"],loc=\"upper center\",fontsize=12);\n",
    "gamma_rad_BEM_rp_average"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "On the plots above, the left shows the real and imaginary parts of the induced field component $E_x(r')$ when an $x$-polarized dipole was placed at $r'=405$nm away from the fiber axis. Results are calculated from BEM and are not normalized properly. When the wave number $k\\approx k_0=\\omega/c$, the values are changing dramatically, despite of a small givin loss to the material. \n",
    "\n",
    "The plot on the right-hand-side is the modified decay rates from the non-guided modes calculated in different methods and scenarios. \n",
    "The red solid line (using the verified \"exact\" mode decomposition method) and the blue stars (using the BEM approach) are the averaged decay rates from the non-guided mode contribution part given as\n",
    "$$\\begin{align}\n",
    "\\frac{\\Gamma_{rad}}{\\Gamma_0} &= 1+ \\frac{\\sum_{i=x,y,z}\\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}{\\sum_{i=x,y,z} \\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_0(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}\\\\\n",
    "&=1+ \\frac{\\sum_{i=x,y,z}\\mathrm{Im}\\left[\\mathbf{e}_i^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_i\\right]}{3\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]}\\\\\n",
    "&= 1+ \\frac{\\mathrm{Tr}\\left\\{\\mathrm{Im}\\left[ \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\right]\\right\\}}{3\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]}\n",
    "\\end{align}$$\n",
    "where $\\mathbf{G}_0=G_0\\mathbb{1}$ with $G_0(\\mathbf{r}',\\mathbf{r}';\\omega)=\\frac{2}{3}k_0^3$ is the Green's function in vacuum with $k_0=\\frac{\\omega}{c}$; and the radiation mode contribution of the induced Green's function tensor in presence of the nanofiber is \n",
    "$$ G_{ind,rad}^{ij}(\\mathbf{r}',\\mathbf{r}')=\\frac{2k_0^2*a.u.}{3\\pi^2}\\int_{-k_0}^{k_0} d\\beta E_j^i(\\mathbf{r}')=\\frac{4k_0^2*a.u.}{3\\pi^2}\\int_{0}^{k_0} d\\beta E_j^i(\\mathbf{r}')$$ with $E_j^i(\\mathbf{r}')$ representing the $i$ electric field component with an atomic unit dipole polarized along $j$ direction ($i,j=1,y,z$).\n",
    "Since the the BEM program uses atomic units and CGS-unit system, the prefactor in the formulas above, $a.u.=\\frac{q}{a_0^2}=1.72\\times 10^7$statvolts/cm, comes from the atomic unit transformation.\n",
    "Compared to the previous averaged LDOS calculation (red curve), the averaged decay rate (dots) calculated based on the local feild componets with dipoles orientated along three basis directions using the BEM program matches our exact solution pretty well.\n",
    "The small mismatch when the dipole position becomes far from the fiber surface may be due to the fact that our \"exact\" decay rate for comparison was actually truncated up to $10$-th order of the non-guided eigen modes of the nanofiber which yields some error for the final result.\n",
    "From what we have calculated earlier for LDOS, the induced non-guided mode contribution part to the decay rate could be negative at some dipole positions which is correctly reflected at the series of numbers as the last output of the calculation above. \n",
    "\n",
    "From the second plot, we also show the non-guided mode induced decay rates that can be coupled to the $\\sigma_\\pm$ and $\\pi$ dipole transitions. \n",
    "As you can see, when the atoms are placed around $200$nm from the nanofiber surface, different dipole transitions don't make a noticeable difference which is no longer true for the square waveguide case as shown in another simulation notebook.\n",
    "In details, we calculate the polarization-dependent decay rates from the non-guided mode contributions by \n",
    "$$\\begin{align}\n",
    "\\frac{\\Gamma_{rad}}{\\Gamma_0} &= 1+ \\frac{\\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}{ \\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_0(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}\n",
    "=1+ \\frac{\\mathrm{Im}\\left[\\mathbf{e}_q^*\\cdot \\mathbf{G}_{ind,rad}(\\mathbf{r}',\\mathbf{r}')\\cdot \\mathbf{e}_q\\right]}{\\mathrm{Im}\\left[G_0(\\mathbf{r}',\\mathbf{r}')\\right]},\n",
    "\\end{align}$$\n",
    "where the three orthogonal dipole transition bases\n",
    "$$\\begin{align}\n",
    "\\mathbf{e}_\\pm &=\\mp \\frac{\\mathbf{e}_{\\tilde{x}}\\pm i\\mathbf{e}_{\\tilde{y}}}{\\sqrt{2}}\\\\\n",
    "\\mathbf{e}_0 &=\\mathbf{e}_{\\tilde{z}}\n",
    "\\end{align}$$\n",
    "correspond to the $\\sigma_\\pm$ and $\\pi$ transitions of the atoms.\n",
    "These basis vectors are quantization-axis dependent, but in our calculation above, we assume the $z$-axis or the waveguide axis is the quantization axis, and hence $\\mathbf{e}_{\\tilde{x}}=\\mathbf{e}_x$, $\\mathbf{e}_{\\tilde{y}}=\\mathbf{e}_y$ and $\\mathbf{e}_{\\tilde{z}}=\\mathbf{e}_z$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Export some variables to a MAT file.\n",
    "#using HDF5,JLD\n",
    "#h5open(\"data/Julia_nanofiber_GFT_decayrates_rad.h5\", \"w\") do h5file\n",
    "#    g=g_create(h5file, \"nanofiber\")\n",
    "#    write(h5file, \"nanofiber/rp_BEM\", rp_BEM)#, \"GFT_rad_ind\",GFT_rad_ind)#,\"omega\",ω,\"gamma0\",gamma0,\"e_dipole_sigmap\",e_dipole_sigmap, \"e_dipole_sigmam\",e_dipole_sigmam,\"e_dipole_pi\",e_dipole_pi,\"gamma_rad_BEM_rp_average\",gamma_rad_BEM_rp_average,\"gamma_rad_BEM_rp_sigmap\",gamma_rad_BEM_rp_sigmap,\"gamma_rad_BEM_rp_sigmam\",gamma_rad_BEM_rp_sigmam,\"gamma_rad_BEM_rp_pi\",gamma_rad_BEM_rp_pi,\"a\",a)\n",
    "#    write(h5file,\"nanofiber/GFT_rad_ind\",GFT_rad_ind)\n",
    "#end\n",
    "#save(\"data/Julia_nanofiber_GFT_decayrates_rad.jld\",\"rp_BEM\",rp_BEM,\"imGFT_rad_ind\",imag(GFT_rad_ind),\"omega0\",ω)\n",
    "using MAT\n",
    "matopen(\"data/D2/Julia_nanofiber_GFT_decayrates_rad_D2.mat\", \"w\") do matfile\n",
    "    write(matfile,\"omega0\",ω)\n",
    "    write(matfile,\"rp_BEM\",collect(rp_BEM))\n",
    "    write(matfile,\"gamma0\",gamma0)\n",
    "    write(matfile,\"e_dipole_sigmap\",e_dipole_sigmap)\n",
    "    write(matfile,\"e_dipole_sigmam\",e_dipole_sigmam)\n",
    "    write(matfile,\"e_dipole_pi\",e_dipole_pi)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_average\",gamma_rad_BEM_rp_average)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_sigmap\",gamma_rad_BEM_rp_sigmap)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_sigmam\",gamma_rad_BEM_rp_sigmam)\n",
    "    write(matfile,\"gamma_rad_BEM_rp_pi\",gamma_rad_BEM_rp_pi)\n",
    "    write(matfile,\"a\",a)\n",
    "    write(matfile,\"GFT_rad_rp\",GFT_rad_ind)\n",
    "    write(matfile,\"Gxx_rad_rp\",Gxx_rad_ind)\n",
    "    write(matfile,\"Gxy_rad_rp\",Gxy_rad_ind)\n",
    "    write(matfile,\"Gxz_rad_rp\",Gxz_rad_ind)\n",
    "    write(matfile,\"Gyx_rad_rp\",Gyx_rad_ind)\n",
    "    write(matfile,\"Gyy_rad_rp\",Gyy_rad_ind)\n",
    "    write(matfile,\"Gyz_rad_rp\",Gyz_rad_ind)\n",
    "    write(matfile,\"Gzx_rad_rp\",Gzx_rad_ind)\n",
    "    write(matfile,\"Gzy_rad_rp\",Gzy_rad_ind)\n",
    "    write(matfile,\"Gzz_rad_rp\",Gzz_rad_ind)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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